The Spin Structure of the Nucleon

Abstract

This article reviews our present understanding of QCD spin physics: the proton spin puzzle and new developments aimed at understanding the transverse structure of the nucleon. We discuss present experimental investigations of the nucleon's internal spin structure, the theoretical interpretation of the different measurements and the open questions and challenges for future investigation.

Review, 43 pages, 23 figures, to appear in Reviews of Modern Physics

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• Determination of the Bjorken Sum and Strong Coupling from Polarized Structure Functions
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• Transverse-Spin and Transverse-Momentum Effects in High-Energy Processes
• The Spin Structure of the Proton
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• Polarised Quark Distributions in the Nucleon from Semi-Inclusive Spin Asymmetries
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• QCD Analysis of Polarized Deep Inelastic Scattering Data
• Deeply Virtual Compton Scattering off the neutron
• Experimental investigation of transverse spin asymmetries in muon-p SIDIS processes: Sivers asymmetries
• Transverse spin structure of the nucleon from lattice QCD simulations
• Single Transverse Spin Asymmetries of Identified Charged Hadrons in Polarized p+p Collisions at $\sqrt{s}$ = 62.4 GeV
• Quark helicity distributions from longitudinal spin asymmetries in muon-proton and muon-deuteron scattering
• A measurement of the Q^2, W and t dependences of deeply virtual Compton scattering at HERA
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• Measurement of the Spin Asymmetry in the Photoproduction of Pairs of High-pT Hadrons at HERMES
• Measurement of Parton Distributions of Strange Quarks in the Nucleon from Charged-Kaon Production in Deep-Inelastic Scattering on the Deuteron
• Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs
• Sivers and Boer-Mulders observables from lattice QCD
• A Next-to-Leading Determination of the Singlet Axial Charge and the Polarized Gluon Content of the Nucleon
• Measurement of the $x$- and $Q^2$-Dependence of the Asymmetry $A_1$ on the Nucleon
• A statistical approach for polarized parton distributions
• The Spin Structure of the Nucleon in the Asymptotic Limit
• Precision Measurement of the Neutron Spin Asymmetry $A_1^n$ and Spin-Flavor Decomposition in the Valence Quark Region
• Experimental investigation of transverse spin asymmetries in muon-p SIDIS processes: Collins asymmetries
• Measurement of Deeply Virtual Compton Scattering with a Polarized Proton Target
• A strategy towards the extraction of the Sivers function with TMD evolution
• Interplay of Spin and Orbital Angular Momentum in the Proton
• The HERMES Dual-Radiator Ring Imaging Cerenkov Detector
• Inclusive cross section and double helicity asymmetry for pi^0 production in p+p collisions at sqrt(s) = 62.4 GeV
• Flavor decomposition of the sea quark helicity distributions in the nucleon from semi-inclusive deep-inelastic scattering
• Observation of transverse polarization asymmetries of charged pion pairs in e+e- annihilation near sqrt s=10.58 GeV
• Two-hadron interference fragmentation functions. Part I: general framework
• Measurement of single-spin azimuthal asymmetries in semi-inclusive electroproduction of pions and kaons on a longitudinally polarised deuterium target
• The Beam--Charge Azimuthal Asymmetry and Deeply Virtual Compton Scattering
• Longitudinal Polarized Parton Densities Updated
• Flexible Parametrization of Generalized Parton Distributions from Deeply Virtual Compton Scattering Observables
• First glances at the transversity parton distribution through dihadron fragmentation functions
• On Gauge-Invariant Decomposition of Nucleon Spin
• Measurement of Single and Double Spin Asymmetries in Deep Inelastic Pion Electroproduction with a Longitudinally Polarized Target
• The Boer-Mulders effect in unpolarized SIDIS: an analysis of the COMPASS and HERMES data on the $\cos 2\varphi$ asymmetry
• Constraining quark angular momentum through semi-inclusive measurements
• Strangeness Contribution to the Proton Spin from Lattice QCD
• Measurement of Angular Distributions of Drell-Yan Dimuons in p + d Interaction at 800 GeV/c
• The HERMES Polarized Hydrogen and Deuterium Gas Target in the HERA Electron Storage Ring
• Transverse spin effects in hadron-pair production from semi-inclusive deep inelastic scattering
• Intrinsic quark transverse momentum in the nucleon from lattice QCD
• A critique of the angular momentum sum rules and a new angular momentum sum rule
• Jet Properties from Dihadron Correlations in p+p Collisions at sqrt(s)=200 GeV
• The gluon spin contribution to the proton spin from the double helicity asymmetry in inclusive pi^0 production in polarized p+p collisions at sqrt(s)=200 GeV
• Calculation of TMD Evolution for Transverse Single Spin Asymmetry Measurements
• Beam-helicity and beam-charge asymmetries associated with deeply virtual Compton scattering on the unpolarised proton
• The RHIC SPIN Program: Achievements and Future Opportunities
• The target asymmetry in hard vector-meson electroproduction and parton angular momenta
• Status of the Proton Spin Problem
• Determination of gluon polarization from deep inelastic scattering and collider data
• Transverse Single-Spin Asymmetry and Cross-Section for pi0 and eta Mesons at Large Feynman-x in Polarized p+p Collisions at sqrt(s)=200 GeV
• The Longitudinal Polarimeter at HERA
• Measurement of Azimuthal Asymmetries With Respect To Both Beam Charge and Transverse Target Polarization in Exclusive Electroproduction of Real Photons
• First extraction of Interference Fragmentation Functions from e+e- data
• Azimuthal distributions of charged hadrons, pions, and kaons produced in deep-inelastic scattering off unpolarized protons and deuterons
• Flavour Separation of Helicity Distributions from Deep Inelastic Muon-Deuteron Scattering
• Evidence for a Transverse Single-Spin Asymmetry in Leptoproduction of pi+pi- Pairs
• Semi-Inclusive Deep Inelastic Scattering processes from small to large P_T
• Collins effect in semi-inclusive deeply inelastic scattering and in electron positron annihilation
• Geometrical approach to the proton spin decomposition
• Measurement of double-spin asymmetries associated with deeply virtual Compton scattering on a transversely polarized hydrogen target
• Gluon Spin in the Nucleon
• Leading and Next-to-Leading Order Gluon Polarisation in the Nucleon and Longitudinal Double Spin Asymmetries from Open Charm Muoproduction
• On the Origin of Model Relations among Transverse-Momentum Dependent Parton Distributions
• The (alpha_s)^3 approximation of Quantum Chromodynamics to the Ellis-Jaffe sum rule
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• Target Independence of the Emc-SMC Effect
• Leading-Order Determination of the Gluon Polarization from high-$p_T$ Hadron Electroproduction
• The nucleon's octet axial-charge g_A^8 with chiral corrections
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• Effect of Orbital Angular Momentum on Valence-Quark Helicity Distributions
• Cross section and double helicity asymmetry for eta mesons and their comparison to neutral pion production in p+p collisions at sqrt(s)=200 GeV
• Beam-Target Double Spin Asymmetry A_LT in Charged Pion Production from Deep Inelastic Scattering on a Transversely Polarized He-3 Target at 1.4<Q^2<2.7 GeV^2
• Leading order determination of the gluon polarisation from DIS events with high-p_T hadron pairs
• Polarized Parton Densities in the Nucleon
• Measurement of the parity-violating longitudinal single-spin asymmetry for $W^{\pm }$ boson production in polarized proton-proton collisions at $\sqrt{s}=500$GeV
• On the controversy concerning the definition of quark and gluon angular momentum
• Light-flavor sea-quark distributions in the nucleon in the SU(3) chiral quark soliton model (I) -- phenomenological predictions --
• Single Spin Asymmetry $A_N$ in Polarized Proton-Proton Elastic Scattering at $\sqrt{s}=200$ GeV
• The Spin Dependence of Diffractive Processes and Implications for the Small $x$ Behaviour of $g_1$ and the Spin Content of the Nucleon
• Global fitting of single spin asymmetry: an attempt
• Measurement of Angular Distributions of Drell-Yan Dimuons in $p+p$ Interactions at 800 GeV/c
• Perturbative Evolution and Regge Behaviour
• Separation of contributions from deeply virtual Compton scattering and its interference with the Bethe--Heitler process in measurements on a hydrogen target
• Gluons and the eta' nucleon coupling constant
• Naive time-reversal odd phenomena in semi-inclusive deep-inelastic scattering from light-cone constituent quark models
• Longitudinal double-spin asymmetry and cross section for inclusive neutral pion production at midrapidity in polarized proton collisions at sqrt(s) = 200 GeV
• Extracting Boer-Mulders functions from $p+D$ Drell-Yan processes
• Understanding the proton's spin structure
• Constraints on the $\tilde{H}$ Generalized Parton Distribution from Deep Virtual Compton Scattering Measured at HERMES
• Local Two-Photon Couplings and the J=0 Fixed Pole in Real and Virtual Compton Scattering
• Mesonic Corrections to the Shape of Quark Distributions
• Updating Boer-Mulders functions from unpolarized pd and pp Drell-Yan data
• Measurement of azimuthal asymmetries associated with deeply virtual Compton scattering on an unpolarized deuterium target
• Gluon Polarisation in the Nucleon and Longitudinal Double Spin Asymmetries from Open Charm Muoproduction
• Helicity Parton Distributions at a Future Electron-Ion Collider: A Quantitative Appraisal
• The small $x$ behaviour of $g_1$
• Exclusive rho-0 electroproduction on transversely polarized protons
• Strange Quark Contribution to the Vector and Axial Form Factors of the Nucleon: Combined Analysis of G0, HAPPEx, and Brookhaven E734 Data
• The Gauge-Invariant Angular Momentum Sum-Rule for the Proton
• The flavour asymmetry of polarized anti-quarks in the nucleon
• Polarized light-antiquark distributions in a meson-cloud model
• Azimuthal asymmetries of charged hadrons produced by high-energy muons scattered off longitudinally polarised deuterons
• Measurement of azimuthal asymmetries associated with deeply virtual Compton scattering on a longitudinally polarized deuterium target
• sPHENIX: An Upgrade Concept from the PHENIX Collaboration
• Elastic Scattering at the LHC
• Insights on non-perturbative aspects of TMDs from models
• Heavy-quark axial charges to non-leading order
• Spin structure functions of 3He at finite Q^2
• Exclusive rho^0 muoproduction on transversely polarised protons and deuterons
• Beam-Induced Nuclear Depolarisation in a Gaseous Polarised Hydrogen Target
• Azimuthal asymmetries of charged hadrons produced in high-energy muon scattering off longitudinally polarised deuterons
• TMD PDFs: a Monte Carlo implementation for the sea quark distribution
• Deuteron spin structure functions in the resonance and DIS regions
• Flavor Structure of the Nucleon Sea
• The Strange Spin of the Nucleon
• Nuclear Polarization of Molecular Hydrogen Recombined on a Non-metallic Surface
• Sivers distribution functions and the latest SIDIS data
• Transverse spin dependent azimuthal asymmetries at COMPASS
• Polarized Gluon Distribution Delta g(x) in the Proton
• Longitudinal and transverse spin asymmetries for inclusive jet production at mid-rapidity in polarized p+p collisions at sqrt{s}=200 GeV
• Transverse Momentum in Semi-Inclusive Polarized Deep Inelastic Scattering and the Spin-Flavor Structure of the Proton
• Charge Symmetry Breaking in Spin Dependent Parton Distributions and the Bjorken Sum Rule
• Reggeon Non-Factorizability and the J=0 Fixed Pole in DVCS
• Local Polarimetry for Proton Beams with the STAR Beam Beam Counters
• Cross sections and double-helicity asymmetries of midrapidity inclusive charged hadrons in p+p collisions at sqrt(s)=62.4 GeV
• Spin constraints on Regge predictions and perturbative evolution in high energy collisions
• Azimuthal asymmetries in the unpolarized SIDIS cross section at COMPASS
• Gluon polarization in the proton
• On the new COMPASS measurement of the deuteron spin-dependent structure function $g_1^d$
• The Spin Structure of the Nucleon: Theoretical Overview
• Unbiased Polarised Parton Distribution Functions and their Uncertainties
• Gluon polarization measurements with inclusive jets at STAR
• Gluon Polarization Measurements from Correlated Probes
• Neutrinos from Pion Decay at Rest to Probe the Proton Strangeness in an Underground Lab
• Updated Report Acceleration of Polarized Protons to 120-150 GeV/c at Fermilab
• Status on the transversity parton distribution: the dihadron fragmentation functions way
• New measurement of DeltaG/G at COMPASS
• Measurements of Double-Spin Asymmetries in SIDIS of Longitudinally Polarized Leptons off Transversely Polarized Protons
• Inserting physics associated with the transverse polarization of the quarks into a standard Monte Carlo generator, without touching the code itself

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• Study of $X_c(3250)$ as a $D_0^{\ast }(2400)N$ molecular state
• Sivers and $\cos 2\varphi$ Asymmetries in Semi-inclusive Deep Inelastic Scattering in Light-front Holographic Model
• Sub-leading twist transverse momentum dependent parton distributions in the light-front quark-diquark model
• High-density gas target at the LHCb experiment
• Target mass corrections in lepton--nucleus DIS: theory and applications to nuclear PDFs
• Twist-4 T-even proton TMDs in the light-front quark-diquark model
• Future tests of parton distributions
• Revisiting quark and gluon polarization in the proton at the EIC
• Unambiguous detection of high energy vortex states via the superkick effect
• Determining the helicity structure of the nucleon at the Electron Ion Collider in China
• Impact of nucleon matrix element uncertainties on the interpretation of direct and indirect dark matter search results
• Deconfinement transition in the revolving bag model
• Transverse spin sum rule of the proton
• Interplay among transversity induced asymmetries in hadron leptoproduction
• Double-Longitudinal Spin Asymmetry in Single-Inclusive Lepton Scattering at NLO
• The spin of the proton in chiral effective field theory
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
• Semi-Inclusive ${\pi }_0$ target and beam-target asymmetries from 6 GeV electron scattering with CLAS
• Inclusive-jet and Di-jet Production in Polarized Deep Inelastic Scattering
• Updating spin-dependent Regge intercepts
• Polarized GPDs and structure functions of $\rho$ meson
• 70 Years of Hyperon Spectroscopy: A review of strange $\Xi$, $\Omega$ baryons, and the spectrum of charmed and bottom baryons
• Deuteron polarizations in the proton-deuteron Drell-Yan process for finding the gluon transversity
• Electron-deuteron DIS with spectator tagging at EIC: Development of theoretical framework
• Fermion EDMs with Minimal Flavor Violation
• Nonperturbative-transverse-momentum effects and evolution in dihadron and direct photon-hadron angular correlations in $p$$+$$p$ collisions at $\sqrt{s}$=510 GeV
• New molecular candidates: X(1910), X(2200), and X(2350)
• Intrinsic Transverse Momentum and Evolution in Weighted Spin Asymmetries
• Generation of Ultrarelativistic Vortex Leptons with Large Orbital Angular Momenta
• QED correction to asymmetry for polarized ep-scattering from the method of the electron structure functions
• Neutron spin structure from polarized deuteron DIS with proton tagging
• Towards three-dimensional nucleon structures at the Electron-Ion Collider in China: A study of the Sivers function
• Gauge Invariant Descriptions of Gluon Polarizations
• Neutron knockout in neutral-current neutrino-oxygen interactions
• Exploring twist-4 chiral-even GPDs in the light-front quark-diquark model
• Nucleon structure functions and longitudinal spin asymmetries in the chiral quark constituent model
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• First Extraction of Transverse Momentum Dependent Helicity Distributions
• Impact of recent COMPASS data on polarized parton distributions and structure functions
• Neutral Current Neutrino-Nucleus Scattering. Theory
• Inclusive and semi-inclusive production of spin-3/2 hadrons in $e^{+}{e}^{-}$ annihilation
• Spin asymmetries for vector boson production in polarized p+p collisions
• Proton spin in leading order of the covariant approach
• Search for $Z_{s1}^{+}$ and $Z_{s2}^{+}$ strangeonium-like structures
• Quark spin content of SU(3) light and singly heavy baryons
• High energy photon polarimeter for astrophysics
• Radiative corrections for the decay ${\Sigma }^0\to \Lambda e^{+}{e}^{-}$
• Differential cross section and photon-beam asymmetry for the gamma p -> pi- Delta++(1232) reaction at forward pi- angles for Egamma=1.5-2.95 GeV
• Gamow-Teller transitions and the spin EMC effect: the Bjorken sum-rule in medium
• Proton spin after 30 years: what we know and what we don't?
• Gluonic Structure of the Constituent Quark
• Nonperturbative transverse-momentum-dependent effects in dihadron and direct photon-hadron angular correlations in $p+p$ collisions at $\sqrt{s}=200$ GeV
• Eta-nucleon and eta-prime-nucleon coupling constants in QCD and the role of gluons
• Parton-shower effects in polarized deep inelastic scattering
• Accurate and efficient spin integration for particle accelerators
• Emergent Gauge Symmetries and Particle Physics
• Transversity distributions from difference asymmetries in semi-inclusive DIS
• Twist-4 proton GTMDs in the light-front quark-diquark model
• Vector and Tensor Spin Polarization for Vector Bosons at Local Equilibrium
• Spin Density Matrix for ${\Omega }^{-}$ and its Polarization Alignment in $\psi (3686)\to {\Omega }^{-}{\bar{\Omega }}^{+}$
• Global Fit of Electron and Neutrino Elastic Scattering Data to Determine the Strange Quark Contribution to the Vector and Axial Form Factors of the Nucleon
• Proton spin: a topological invariant
• Strange quark helicity in the proton from chiral effective theory
• The axial charges of proton within an extended chiral constituent quark model
• Accessing gluon polarization with high-$P_T$ hadrons in SIDIS
• The transverse nucleon single-spin asymmetry for the semi-inclusive production of photons in lepton-nucleon scattering
• Evidence of time evolution in quantum gravity
• Dijet Production in Neutral Current and Charged Current Polarized Deep Inelastic Scattering
• Spin and Polarization in High-Energy Hadron-Hadron and Lepton-Hadron Scattering
• Double longitudinal-spin asymmetries in $J/\psi$ production at RHIC
• Orbital angular momentum of the proton and intrinsic five-quark Fock states
• Effects of Non-Commutativity on Light-Hydrogen-Like Atoms and Proton Radius
• Direct Detection Constraints on Dark Matter Event Rates in Neutrino Telescopes, and Collider Implications
• Kinked tracks from ${\Sigma }^{+}$ baryons as a probe of light quark polarizations
• $Y(4626)$ as a $P$-wave $[cs][\bar{c}\bar{s}]$ tetraquark state
• Tomography of the Rho meson in the QCD Instanton Vacuum: Transverse Momentum Dependent Parton Distribution Functions
• Neutrino flavour as a test of the explosion mechanism of core-collapse supernovae
• Probing the limits of quantum theory with quantum information at subnuclear scales
• Domain-Adversarial Graph Neural Networks for $\Lambda$ Hyperon Identification with CLAS12
• The Proton Spin, Semi-Inclusive processes, and a future Electron Ion Collider
• Semi-inclusive deep inelastic scattering off a tensor-polarized spin-1 target
• Nucleon Structure Functions from the NJL-Model Chiral Soliton
• Basis transformation properties of anomalous dimensions for hard exclusive processes
• Partonic Picture of Generalized Transverse Momentum Distributions
• Collinear Factorization at sub-asymptotic kinematics and validation in a diquark spectator model
• Sea contribution to the charge radii and quadrupole moment of $J^P={\frac{1}{2}}^{+},{\frac{3}{2}}^{+}$ baryons
• Pseudogauge ambiguity in the distributions of energy density, pressure, and shear force inside the nucleon
• Small-x behavior of non-singlet spin structure function and Bjorken sum rule with pQCD correction up to NNLO and Higher twist correction
• Nucleon Structure from Basis Light-Front Quantization : Status and Prospects
• Gauge Invariant Noether's Theorem and The Proton Spin Crisis
• Spin dependence of η meson production in proton-proton collisions close to threshold
• Study of cold and hot nuclear matter effects on jets with direct photon triggered correlations from PHENIX
• Quark and gluon orbital angular momentum: Where are we?
• Mapping the internal structure of hadrons through color and spin effects
• Symmetric point flavour singlet axial vector current renormalization at two loops
• Measurement of the nucleon spin structure functions for 0.01<$Q^2$<1 GeV${}^2$ using CLAS
• Achievements and open issues in the determination of polarized parton distribution functions
• Ideas in transverse spin physics
• Transverse Spin Effects in Future Drell-Yan Experiments
• Investigating the transverse momentum dependent gluon Sivers function in quarkonium production at $pp$ colliders
• Differential Heavy Quark Distributions and Correlations in Longitudinally Polarized Deep-Inelastic Scattering
• Octet and decuplet contribution to the proton self energy
• Highlights from BNL and RHIC 2015
• The Gerasimov-Drell-Hearn sum-rule with nuclear targets
• QCD symmetries and the eta and etaprime in nuclei
• Kotzinian-Mulders effect in semi-inclusive DIS within TMD factorization
• Looking for a vector charmonium-like state $Y$ in $e^{+}{e}^{-}\to \bar{D}{D}_1(2420)+c.c.$
• AAK24: Global QCD analysis on polarized parton distribution in the presence of $A_2$ asymmetry measurements
• Transverse Single Spin Asymmetries in Hadronic Interactions: an experimental overview and outlook
• A Vision of Hadronic Physics
• PHENIX results on jet modification with ${\pi }^0$- and photon-triggered two particle correlations in $p$$+$$p$, $p(d)$+Au, and Au+Au collisions
• Chirality distributions inside baryons in $\mathrm{QC}{\mathrm{D}}_2$
• Measurement of transverse single-spin asymmetries for dijet production in polarized proton-proton collisions at $\sqrt{\mathbf{s}}$ = 200 $\mathrm{GeV}$
• A systematic approach to determine the spectral characteristics of molecular magnets
• Gluonic Distribution in the Constituent Quark and Nucleon Induced by the Instantons
• Transverse Single-Spin Asymmetries of Midrapidity Direct Photons, Neutral Pions, and Eta Mesons in 200 GeV Polarized Proton-Proton Collisions at PHENIX
• Nonperturbative factorization breaking and color entanglement effects in dihadron and direct photon-hadron angular correlations in $p$$+$$p$ and $p$$+$A collisions
• Neutron Spin Structure from e-3He Scattering with Double Spectator Tagging at the Electron-Ion Collider
• On the role of quark orbital angular momentum in the proton spin
• Accessing baryon-antibaryon generalized distribution amplitudes in $e^{\pm }\gamma \to e^{\pm }B\bar{B}$
• Deeply virtual Compton scattering off the neutron
• $J/\psi$ production in proton-proton collisions at Spin Physics Detector energies of the JINR Nuclotron-based Ion Collider fAcility
• Measurements of the Absolute Branching Fraction of the Semileptonic Decay ${\mathbf{\Xi }}^{-}\to \mathbf{\Lambda }{\mathbf{e}}^{-}{\bar{\nu }}_{\mathbf{e}}$ and the Axial Charge of the ${\mathbf{\Xi }}^{-}$
• Observation of $\Xi (1530{)}^0$ Polarization and Determination of Its Electric and Magnetic Moments in $\psi (3686)\to \Xi (1530{)}^0\bar{\Xi }(1530{)}^0$
• Proton Spin and Tensorgluons
• Role of higher twist distributions in the tomography of proton
• Tomography of Pions and Kaons in the QCD Vacuum: Transverse Momentum Dependent Parton Distribution Functions
• Symmetry breaking effects in pion couplings to constituent quark currents
• Spin polarization of $\Lambda$ hyperons in $e^{+}{e}^{-}\to \Lambda \bar{\Lambda }$ at BESIII
• Novel experimental probes of QCD in SIDIS and $e^{+}{e}^{-}$ annihilation
• Quasi-Elastic Neutrino Reactions on Carbon and Lead Nuclei